Superconnection and family Bergman kernels

Xiaonan Ma; Weiping Zhang

doi:10.1016/j.crma.2006.11.013

Differential Geometry

Superconnection and family Bergman kernels
[Superconnexion et noyaux de Bergman en famille]

Présenté par : Jean-Michel Bismut

Xiaonan Ma ¹ ; Weiping Zhang ²

¹ Centre de mathématiques Laurent-Schwartz, UMR 7640 du CNRS, École polytechnique, 91128 Palaiseau cedex, France
² Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, P.R. China

Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 41-44.

Résumé
Abstract

Nous annonçons des résultats sur le développement asymptotique du noyau de Bergman en famille. L'idée principale est d'utiliser le formalisme des superconnexions comme dans la preuve du théorème de l'indice local en famille.

We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection formalism as in the local family index theorem.

Reçu le : 2006-11-06
Accepté le : 2006-11-08
Publié le : 2006-12-11

DOI : 10.1016/j.crma.2006.11.013

Affiliations des auteurs :

Xiaonan Ma ¹ ; Weiping Zhang ²

¹ Centre de mathématiques Laurent-Schwartz, UMR 7640 du CNRS, École polytechnique, 91128 Palaiseau cedex, France
² Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, P.R. China

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     title = {Superconnection and family {Bergman} kernels},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {41--44},
     publisher = {Elsevier},
     volume = {344},
     number = {1},
     year = {2007},
     doi = {10.1016/j.crma.2006.11.013},
     language = {en},
}

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Xiaonan Ma; Weiping Zhang. Superconnection and family Bergman kernels. Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 41-44. doi : 10.1016/j.crma.2006.11.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.013/

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